Related papers: A Note on Perturbations During a Regular Bounce
Budden's energy nonconservation paradox is dispelled herein by recognizing that pole approach to the spatial origin from below in the complex plane can be resolved into a real principal value plus $-i\pi$ times a Dirac delta, the imaginary…
Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within N-soliton train of the nonlinear Schrodinger equation (NLS). Perturbations induced by weak quadratic and periodic external…
In this paper, we investigate a non-interacting scalar field cosmology with an arbitrary potential using the $f$-deviser method that relies on the differentiability properties of the potential. Using this alternative mathematical approach,…
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition…
A major drawback of adiabatic quantum computing (AQC) is fulfilling the energy gap constraint, which requires the total evolution time to scale inversely with the square of the minimum energy gap. Failure to satisfy this condition violates…
We review the doubly gauge invariant formalism of cosmological perturbations in the Randall-Sundrum brane world. This formalism leads to four independent equations describing the evolution of scalar perturbations. Three of these equations…
For nonautonomous linear difference equations in Banach spaces we show that a very general type of dichotomic behavior persists under small enough additive linear perturbations. By using a new approach, we obtain two general robustness…
We study four dimensional non-abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of…
This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
We consider free rotation of a body whose parts move slowly with respect to each other under the action of internal forces. This problem can be considered as a perturbation of the Euler-Poinsot problem. The dynamics has an approximate…
We revisit the question of whether fluctuations in hydrodynamical, adiabatical matter could explain the observed structures in our Universe. We consider matter with variable equation of state $w=p_0/\ep_0$ and a concomitant (under the…
We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ)…
Explorations of the violation of null energy condition (NEC) in cosmology could enrich our understanding of the very early universe and the related gravity theories. Although a fully stable NEC violation can be realized in the ``beyond…
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the…
The limits of the Second Law of Thermodynamics, which reigns undisputed in the macroscopic world, are investigated at the mesoscopic level, corresponding to spatial dimensions of a few microns. An extremely simple isolated system, modeled…
We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set…
We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an…
We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…